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คะแนน ดังนี้ \[ \begin{array}{lllllllllllllll} 9 & 10 & 12 & 12 & 14 & 14 & 15 & 16 & 16 & 16 & 17 & 17 & 18 & 19 & 20 \end{array} \] 1. จงหาควอร์ไทล์ที่ \( 1\left(\mathrm{Q}_{1}\right) \) ควอร์ไทล์ที่ \( 2\left(\mathrm{Q}_{2}\right) \) ควอร์ไทล์ที่ \( 3\left(\mathrm{Q}_{3}\right) \) วิธีคิดตามขั้นตอน 1. หาตำแหน่งที่ จาก \( \mathrm{Q}_{\mathrm{r}}=\frac{r(N+1)}{4} \) โดยหา ตำแหน่งของ \( \mathrm{Q}_{1}, \mathrm{Q}_{2}, \mathrm{Q}_{3} \) 2. จากตำแหน่งที่หาได้ในข้อ 1 ตรงกับข้อมูลในโจทย์เท่าใด วิธีทำ

Ask by Newton Mills. in Thailand
Feb 25,2025

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ควอร์ไทล์ที่ 1 (Q₁) = 12, ควอร์ไทล์ที่ 2 (Q₂) = 16, ควอร์ไทล์ที่ 3 (Q₃) = 17

Solución

เรามีข้อมูลคะแนนเรียงจากน้อยไปมากดังนี้   9 10 12 12 14 14 15 16 16 16 17 17 18 19 20 จำนวนข้อมูลทั้งหมด N = 15   ขั้นตอนที่ 1: หา “ตำแหน่ง” ของ Q₁, Q₂, Q₃ โดยใช้สูตร     Qᵣ = (r (N + 1))/4                       (สำหรับ r = 1, 2, 3) 1. หาค่าตำแหน่งของ Q₁   ตำแหน่งของ Q₁ = (1×(15+1))/4 = 16/4 = 4   ดังนั้น Q₁ อยู่ที่ตำแหน่งที่ 4 ซึ่งข้อมูลตำแหน่งที่ 4 = 12   → Q₁ = 12 2. หาค่าตำแหน่งของ Q₂   ตำแหน่งของ Q₂ = (2×(15+1))/4 = 32/4 = 8   ดังนั้น Q₂ อยู่ที่ตำแหน่งที่ 8 ซึ่งข้อมูลตำแหน่งที่ 8 = 16   → Q₂ = 16 3. หาค่าตำแหน่งของ Q₃   ตำแหน่งของ Q₃ = (3×(15+1))/4 = 48/4 = 12   ดังนั้น Q₃ อยู่ที่ตำแหน่งที่ 12 ซึ่งข้อมูลตำแหน่งที่ 12 = 17   → Q₃ = 17 สรุป   Q₁ = 12  Q₂ = 16  Q₃ = 17

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เพื่อหาควอร์ไทล์ที่ \( Q_1, Q_2, Q_3 \) เราจะทำตามขั้นตอนที่คุณกำหนดค่ะ **ขั้นตอนที่ 1: หาตำแหน่งของควอร์ไทล์** 1. จำนวนข้อมูล \( N = 15 \) (ข้อมูลทั้งหมด 15 ตัว) 2. หาตำแหน่งของ \( Q_1 \): \[ Q_1 = \frac{1(15+1)}{4} = \frac{16}{4} = 4 \] 3. หาตำแหน่งของ \( Q_2 \): \[ Q_2 = \frac{2(15+1)}{4} = \frac{32}{4} = 8 \] 4. หาตำแหน่งของ \( Q_3 \): \[ Q_3 = \frac{3(15+1)}{4} = \frac{48}{4} = 12 \] **ขั้นตอนที่ 2: เช็คค่าที่ตำแหน่งที่หามา** - สำหรับ \( Q_1 \) ที่ตำแหน่งที่ 4 จะได้ค่า = 12 - สำหรับ \( Q_2 \) ที่ตำแหน่งที่ 8 จะได้ค่า = 16 - สำหรับ \( Q_3 \) ที่ตำแหน่งที่ 12 จะได้ค่า = 17 ดังนั้น ค่าของควอร์ไทล์จะเป็น: - \( Q_1 = 12 \) - \( Q_2 = 16 \) - \( Q_3 = 17 \)

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